Paper-sheet stacking apparatuses are apparatuses that collect and stack, in a standing position, paper sheets such as mail items transported at high speed. Any apparatus of this type comprises a holding unit for holding paper sheets, a movable backup plate, a pushing roller and a supporting guide. The backup plate is arranged, touching the paper sheet that is an endmost sheet of the paper-sheet stack held in the holding unit. The backup plate moves in the direction the paper sheets are stacked, in accordance with the number of the paper sheets stacked, and therefore pushes the paper-sheet stack in the direction the paper sheets are stacked. The pushing roller is located at some distance from the backup plate and touches, in rolling contact, the other endmost paper sheet of the paper-sheet stack, cooperating with the backup plate to clamp the paper-sheet stack. The pushing roller receives the paper sheet next to the other endmost paper sheet, between it and the other endmost paper sheet, and then pushes the paper sheet next to the other endmost paper sheet into the end of the paper-sheet stack.
In recent years, paper sheets (document sheets) that can be processed in the paper-sheet processing apparatus such as a mail processing apparatus have been increasing in size. Further, these paper sheets are increasing in thickness, year by year. In the paper-sheet stacking apparatus described above, the pressure applied to the backup plate is constant, and the backup member may be flicked because of the weight of the paper-sheet stack when a thick paper sheet, for example, is fed, In this case, the thick paper sheet is pushed away, and cannot be stacked. To prevent this event, the pressured applied to the backup plate may be increased. If the pressure is increased, however, the pressure for stacking paper sheets will not be mitigated. As a result, the pressure the pushing roller applies to the paper-sheet stack rises, making it difficult to feed paper sheets onto the paper-sheet stack.